Results 271 to 280 of about 1,464,296 (288)
Some of the next articles are maybe not open access.
The American Mathematical Monthly, 1957
(1957). The Exponential Function. The American Mathematical Monthly: Vol. 64, No. 3, pp. 158-160.
openaire +2 more sources
(1957). The Exponential Function. The American Mathematical Monthly: Vol. 64, No. 3, pp. 158-160.
openaire +2 more sources
ESTIMATING EXPONENTIAL UTILITY FUNCTIONS
Agricultural Economics Research, 1978The exponential utility function for money has long attracted attention from theorists because it exhibits nonincreasing absolute risk aversion. Also, under certain conditions, it generates an expected utility function that is maximizable in a quadratic program. However, this functional form presents estimation problems.
Buccola, Steven T. +3 more
openaire +4 more sources
2014
By now we know Euler’s number \(\mathrm{e} =\mathrm{ e}^{1}\) quite well. In this chapter we define the exponential function \(\mathrm{e}^{x}\) for any x ∈ R, and its inverse the natural logarithmic function ln(x), for x > 0. (In the first section of the chapter we take a concise approach to the exponential function; in the second section we do things ...
openaire +2 more sources
By now we know Euler’s number \(\mathrm{e} =\mathrm{ e}^{1}\) quite well. In this chapter we define the exponential function \(\mathrm{e}^{x}\) for any x ∈ R, and its inverse the natural logarithmic function ln(x), for x > 0. (In the first section of the chapter we take a concise approach to the exponential function; in the second section we do things ...
openaire +2 more sources
Double exponential sums with exponential functions
International Journal of Number Theory, 2017We obtain several estimates for double rational exponential sums modulo a prime [Formula: see text] with products [Formula: see text] where both [Formula: see text] and [Formula: see text] run through short intervals and [Formula: see text] is fixed integer.
Igor E. Shparlinski, Kam Hung Yau
openaire +2 more sources
EXCESSES OF SYSTEMS OF EXPONENTIAL FUNCTIONS [PDF]
Mathematics of the USSR-Izvestiya, 1977 Conditions on the closeness of real sequences {λn} and {μn} are studied which imply the equality of the excesses of the systems {exp(iλnx)} and {exp(iμnx)} in the space L2(−a, a). A theorem is formulated in terms of the difference of the sequences {λn} and {μn} enumerating the functions.
openaire +4 more sources
1995
It is a general problem to determine the continued fractions for values of classical functions suitably normalized. We shall describe a solution of this problem in a very special case which will allow us in particular to get the continued fraction for e.
openaire +2 more sources
It is a general problem to determine the continued fractions for values of classical functions suitably normalized. We shall describe a solution of this problem in a very special case which will allow us in particular to get the continued fraction for e.
openaire +2 more sources
1983
Let z denote the identity map on C. For every non-negative integer n, we define a polynomial function E n by $$ {E_n} = \sum\limits_{{k = 0}}^n {\frac{1}{{k!}}{z^k}} $$ Given an arbitrary complex number c, let n be such that n + 1 ≧ 2|c|, and let q be an arbitrary positive integer.
openaire +2 more sources
Let z denote the identity map on C. For every non-negative integer n, we define a polynomial function E n by $$ {E_n} = \sum\limits_{{k = 0}}^n {\frac{1}{{k!}}{z^k}} $$ Given an arbitrary complex number c, let n be such that n + 1 ≧ 2|c|, and let q be an arbitrary positive integer.
openaire +2 more sources
Exponential and Logarithmic Functions I
1971In the preceding chapter we carefully avoided applying calculus to exponential and logarithmic functions although these functions are of fundamental importance for all kinds of mathematical and statistical treatment in the life sciences.
openaire +2 more sources
Exponential Functions of Matrices
2020In Chap. 12, we dealt with a function of matrices. In this chapter we study several important definitions and characteristics of functions of matrices. If elements of matrices consist of analytic functions of a real variable, such matrices are of particular importance.
openaire +2 more sources
Logarithmic and Exponential Functions
2013The entire algebra of logarithm is based on the following definition: The logarithm of a number a to the base b is a number c such that a can be expressed as b to the power c.
openaire +2 more sources